Transcript Chapter 26 Direct-Current Circuits

Chapter 26
Direct-Current Circuits
• Study resistors in series and parallel
• Consider Kirchoff’s Rules
• The design and use of electronic measuring
instruments
• R-C circuits
• The applications of circuits in household wiring
Resistors in Series and Parallel
Resistors in Series
Vab  Vax  Vxy  V yb  IR1  IR2  IR3
Vab  I ( R1  R2  R3 )  IReq
Req  R1  R2  R3
Figure 26-1
Resistors in Parallel
Figure 26-1
Vab Vab Vab


R1 R2 R3
 1 
1
1
1 

I  Vab  
   Vab 
R 
 R1 R2 R3 
 eq 
1
1
1
1
 

Req R1 R2 R3
I  I1  I 2  I 3 
Chapter 26
2
Series and parallel combination resistors
– Consider Problem-Solving Strategy 26.1.
– Follow Example 26.1 guided by Figure 26.3 below.
– Follow Example 26.2.
Kirchoff’s Rules I—junctions
• The algebraic sum of the currents into any junction is zero.
Kirchhoff’s Laws
Kirchhoff’s Current Law
Proof
Charge can’t build up at the junction.
Figure 26-7
Kirchhoff’s Current Law - Example
Figure 26-8
Chapter 26
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Kirchoff’s Rules II—loops
• The algebraic sum of the potential differences in any loop,
including those associated with emfs and those of resistive
elements, must equal zero.
Kirchhoff’s Voltage Law – Two Loop Example
Loop 1
Loop 1
1  I1r1  I1R1  I 3 R3  0
1  I1r1  I1R1  ( I1  I 2 ) R3  0
Loop 2
Loop 2
 2  I 2 r2  I 3 R3  I 2 R2  0
 2  I 2 r2  ( I1  I 2 ) R3  I 2 R2  0
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Kirchhoff’s Laws - A Single Loop Circuit
Example 26-3
a) Solve for I
b) Solve for Vab
c) Solve for power output of
the emf of each battery
Figure 26-10
Chapter 26
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Kirchoff’s Rules III—examples and strategy
• Read through Problem-Solving Strategy 26.2. Figure 26.9
illustrates this strategy.
• Refer to Example 26.3, illustrated by Figure 26.10.
Kirchoff’s Rules IV—examples
•
•
•
•
Refer to Example 26.4, illustrated by Figure 26.11.
Consider Example 26.5.
Refer to Example 26.6, illustrated by Figure 26.12.
Review Example 26.7.
R-C Circuits (Chapter 26, Sec 4)
Charging a Capacitor

R
0.37 I0
  vab  vbc
C
q  vbcC
vbc 
vab  iR
i
0.63 Qf
q
C
vab
R
Time Constant
Figure 26-20
Figure 26-21
Chapter 26
  RC
(26-14)
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R-C Circuits (Chapter 26, Sec 4)
Discharging a Capacitor
0  vab  vbc
vab  vbc
Q0
RC
q  vbcC
vbc 
vab  iR
i
q
C
vab
R
Time Constant
  RC
Figure 26-22
(26-14)
Figure 26-23
Chapter 26
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D’Arsonval’s galvanometer
• We’ll call it simply “meter” henceforth.
• The meter is a coil of wire mounted next to a permanent
magnet. Any current passing through the coil will induce
magnetism in the coil. The interaction of the new
electromagnetism and the permanent magnet will move the
meter indicator mounted to the coil.
The Ammeter and Voltmeter
• The ammeter (sometimes prefixed with milli or micro because
the currents to be measured are routinely thousandths or
millionths of an ampere) may be used to measure current OR
voltage. A shunt resistor makes this conversion as shown below
in Figure 26.15.
• Consider Example 26.8 to follow a current example. Consider
Example 26.9 to follow a voltage example.
Ammeter Design
Vab = Vab
Ifs Rc = (Ia – Ifs) Rsh
Ifs = 1 mA Rc = 50 ohm
Ia = 50 mA Rsh = ?
Voltmeter Design
Vab = Ifs (Rc + Rs )
Solve for Rs
Rs= (Vab - Ifs Rc)/ Ifs
Ifs = 1 mA Rc = 20 ohm
Vab = 10 v
Rs = ?
Ohmmeters and digital multimeters
• An ohmmeter is designed specifically to measure resistance.
• Refer to Figure 26.17 and Figure 26.18 below to see an
ohmmeter wiring diagram and a photograph of a digital
multimeter. The multimeter can measure current, voltage, or
resistance over a wide range.
Power Distribution Systems
240-V line
black, red Neutral
Black
White
120 v
One phase of the 240-V line
We buy energy from the Power Company, not power
kW x time = watt-seconds = Joules
1 kWh = (1000W) (3600 s ) = 3.6 x 106 W-s = 3.6 x 106 J
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Fuses, circuit breakers, and GFI
• A fuse will melt and a breaker will
open the circuit if maximum
current is reached. See Figure
26.26.
• GFI stops further current flow
when a sudden drop in resistance
indicates that someone has offered
a new path to ground. I don’t know
if it will save this worker we see in
Figure 26.27 who didn’t use a
grounded drill.
The wiring diagram for a typical kitchen
– Consider Figure 26.28 below.
– Follow Example 26.14.
Average Retail Price of Electricity
cents per kilowatt-hour
Census Division
and State
Commercial1
Residential
Nov-07
Nov-06
Nov-07
Industrial1
Nov-06
Nov-07
Nov-06
New England
16.18
15.58
14.19
13.78
12.75
11.44
Connecticut
18.33
16.92
14.91
14.24
12.46
12.08
Maine
15.42
14.06
13.04
11.91
12.12
9.45
Massachusetts
15.69
15.74
14.38
14.22
14.01
12.53
14.8
14.22
13.26
13.28
12.32
10.78
Rhode Island
14.62
14.34
13.2
12.81
12.18
12.28
Vermont
14.35
13.57
12.36
11.84
8.79
8.31
New Hampshire
U.S. Total
10.69
10.18
9.6
9.24
6.22
6.04
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